Steinberg unitary Leibniz algebras (Q2484244)

An associative version of a Leibniz algebra [\textit{J.-L.\ Loday}, Enseign. Math. (2) 39, 269--293 (1993; Zbl 0806.55009)] is called a dialgebra [\textit{J.-L.\ Loday}, Lect. Notes Math. 1763, 7--66 (2001; Zbl 0999.17002)]. Given a unital associative algebra \(A\) with an (anti-) involution \(-\) and \(\gamma=(\gamma_1,\ldots,\gamma_n)\), where \(\gamma_1\not=0\in A\), write \(\text{stu}(n,A,-,\gamma)\) (resp.\ \(\text{stul}(n,A,-,\gamma)\)). The authors consider \(\text{stul}(n,D,-,\gamma)\) over a unital dialgebra \(D\) with involution \(-\) and study its properties. In particular, some results on its central extension, as in the Steinberg unitary Leibniz Lie algebras, are presented.